The present invention relates to apparatus and method for controlling a controlled system, or plant, such as an air/fuel ratio sensor for sensing an air/fuel ratio of an engine of a motor vehicle.
There has been proposed various air/fuel ratio sensing systems (Japanese patent provisional publication No. 62-15451, for example). In one conventional example, there are provided two sensing elements each of which is composed of an oxygen ion conductive solid electrolyte plate sandwiched between a pair of electrodes of porous material. This conventional air/fuel ratio sensing device uses one of the sensing elements as an oxygen concentration cell element, and the other as an oxygen pump element, and outputs an air/fuel ratio signal corresponding to the oxygen concentration of an exhaust gas mixture acting as a disturbance.
FIG. 6 schematically shows this conventional air/fuel ratio sensing device. This device includes a sensor section for sensing an air/fuel ratio, and a controller section for controlling the sensor section. The sensor section has a transfer function Gss, and the controller section has a transfer function Gc. In FIG. 6, V.sub.B is a voltage of the oxygen concentration cell element, and I.sub.C is a pump current. A current IA.times.sin .omega.1 t corresponding to the oxygen concentration of the engine exhaust gas mixture is applied as a disturbance to a junction point P3 between an output terminal of the controller section and an input terminal of the sensor section.
FIG. 7 is a Bode diagram for the sensor section. Because the sensor section has a high order lag, the conventional air/fuel ratio sensing device tends to become unstable. The control system oscillates if the gain of the frequency characteristic for a loop transfer function Gc.times.Gss of the controlled system and the controller is greater than zero dB at the frequency at which the phase angle is -180.degree. (phase leg). Three Bode diagrams (A), (B) and (C) in FIG. 8 shows frequency characteristics for the transfer function Gss of the sensor section, the transfer function Gc of the controller section, and the loop transfer function Gss.times.Gc of the conventional system. In the Bode diagram (A) of FIG. 8, g10 is a gain line, and g11 is a phase line for the sensor section. In the Bode diagram (B), a graph g13 is a gain line obtained when the gain of the controller section is equal to G1, and G12 is a gain line obtained when the gain is equal to G2. A graph g14 is a phase line for the controller section. The Bode diagram (C) shows a gain line g15 for the loop transfer function G1.times.Gss, a gain line g16 for the loop transfer function G2.times.Gss, and a phase line g17. The gain of g16 is equal to or lower than zero dB at a point P2 at which the phase angle of the loop transfer function Gss.times.Gc reaches -180.degree.. Therefore, the control system is stable when the gain of the controller section is set equal to G2.
However, it is difficult to set the controller gain at such an appropriate value as to prevent oscillation especially in the air/fuel ratio sensing device in which the sensor characteristic Gss is greatly influenced by the ambient atmosphere and the sensor temperature, and parameter identification is difficult. In the Bode diagram of FIG. 7, g1 is a phase line and g2 is a gain line. The phase and gain of the sensor section are varied by the ambient atmosphere and the sensor temperature as shown by hatched areas, are 1 and are 2 in FIG. 7, respectively. The influences are remarkable especially in a high frequency range.